Given integers t < k < v and lambda > 0, a t-design or t-(v,k,lambda) design is an incidence structure of points X and blocks B,
where X is a set of v points, B is a collection of k-subsets of X, with the property that any t points are contained
in exactly lambda blocks. If lambda = 1 and t >= 2, then a t-design is also called a Steiner system S(t,k,v).

Many designs are highly symmetric structures, having large automorphism groups. In particular, the Mathieu groups,
which were the first discovered sporadic finite simple groups, turn up as the automorphism groups of the Witt designs.